{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import cufflinks as cf\n",
    "# 根据数据，利用指数平滑法预测2005年和2006年的销售量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "outputs": [
    {
     "data": {
      "text/plain": "    Year      Q\n0   1993   54.0\n1   1994   50.0\n2   1995   52.0\n3   1996   67.0\n4   1997   82.0\n5   1998   70.0\n6   1999   89.0\n7   2000   88.0\n8   2001   84.0\n9   2002   98.0\n10  2003   91.0\n11  2004  106.0\n12  2005    NaN\n13  2006    NaN",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Year</th>\n      <th>Q</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1993</td>\n      <td>54.0</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1994</td>\n      <td>50.0</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1995</td>\n      <td>52.0</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1996</td>\n      <td>67.0</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1997</td>\n      <td>82.0</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1998</td>\n      <td>70.0</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1999</td>\n      <td>89.0</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>2000</td>\n      <td>88.0</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>2001</td>\n      <td>84.0</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>2002</td>\n      <td>98.0</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>2003</td>\n      <td>91.0</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>2004</td>\n      <td>106.0</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>2005</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>2006</td>\n      <td>NaN</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source_df = pd.read_excel('7-7.xlsx')\n",
    "source_df"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "source": [
    "alpha = 0.45\n",
    "source_df.loc[:11,'E1'] = source_df.loc[:,'Q'].ewm(alpha=alpha , adjust = False).mean()\n",
    "source_df.loc[:11,'E2'] = source_df.loc[:,'E1'].ewm(alpha=0.45 , adjust = False).mean()\n",
    "source_df.loc[:11,'at'] = source_df.apply(lambda x: 2*x['E1'] - x['E2'] , axis=1)\n",
    "source_df.loc[:11,'bt'] = source_df.apply(lambda x: alpha / (1-alpha)*(x['E1'] - x['E2']) , axis=1)\n",
    "\n",
    "source_df"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "    Year      Q         E1         E2          at        bt\n0   1993   54.0  54.000000  54.000000   54.000000  0.000000\n1   1994   50.0  52.200000  53.190000   51.210000 -0.810000\n2   1995   52.0  52.110000  52.704000   51.516000 -0.486000\n3   1996   67.0  58.810500  55.451925   62.169075  2.747925\n4   1997   82.0  69.245775  61.659158   76.832393  6.207233\n5   1998   70.0  69.585176  65.225866   73.944487  3.566708\n6   1999   89.0  78.321847  71.119057   85.524636  5.893191\n7   2000   88.0  82.677016  76.320139   89.033893  5.201081\n8   2001   84.0  83.272359  79.448638   87.096080  3.128499\n9   2002   98.0  89.899797  84.151660   95.647935  4.703022\n10  2003   91.0  90.394889  86.961113   93.828664  2.809453\n11  2004  106.0  97.417189  91.666347  103.168031  4.705234\n12  2005    NaN        NaN        NaN         NaN       NaN\n13  2006    NaN        NaN        NaN         NaN       NaN",
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     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "data": {
      "text/plain": "    Year      Q         E1         E2          at        bt          yt\n0   1993   54.0  54.000000  54.000000   54.000000  0.000000         NaN\n1   1994   50.0  52.200000  53.190000   51.210000 -0.810000   54.000000\n2   1995   52.0  52.110000  52.704000   51.516000 -0.486000   50.400000\n3   1996   67.0  58.810500  55.451925   62.169075  2.747925   51.030000\n4   1997   82.0  69.245775  61.659158   76.832393  6.207233   64.917000\n5   1998   70.0  69.585176  65.225866   73.944487  3.566708   83.039625\n6   1999   89.0  78.321847  71.119057   85.524636  5.893191   77.511195\n7   2000   88.0  82.677016  76.320139   89.033893  5.201081   91.417828\n8   2001   84.0  83.272359  79.448638   87.096080  3.128499   94.234974\n9   2002   98.0  89.899797  84.151660   95.647935  4.703022   90.224579\n10  2003   91.0  90.394889  86.961113   93.828664  2.809453  100.350957\n11  2004  106.0  97.417189  91.666347  103.168031  4.705234   96.638118\n12  2005    NaN        NaN        NaN         NaN       NaN  107.873265\n13  2006    NaN        NaN        NaN         NaN       NaN  112.578499",
      "text/html": "<div>\n<style scoped>\n    .dataframe tbody tr th:only-of-type {\n        vertical-align: middle;\n    }\n\n    .dataframe tbody tr th {\n        vertical-align: top;\n    }\n\n    .dataframe thead th {\n        text-align: right;\n    }\n</style>\n<table border=\"1\" class=\"dataframe\">\n  <thead>\n    <tr style=\"text-align: right;\">\n      <th></th>\n      <th>Year</th>\n      <th>Q</th>\n      <th>E1</th>\n      <th>E2</th>\n      <th>at</th>\n      <th>bt</th>\n      <th>yt</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>1993</td>\n      <td>54.0</td>\n      <td>54.000000</td>\n      <td>54.000000</td>\n      <td>54.000000</td>\n      <td>0.000000</td>\n      <td>NaN</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1994</td>\n      <td>50.0</td>\n      <td>52.200000</td>\n      <td>53.190000</td>\n      <td>51.210000</td>\n      <td>-0.810000</td>\n      <td>54.000000</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>1995</td>\n      <td>52.0</td>\n      <td>52.110000</td>\n      <td>52.704000</td>\n      <td>51.516000</td>\n      <td>-0.486000</td>\n      <td>50.400000</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>1996</td>\n      <td>67.0</td>\n      <td>58.810500</td>\n      <td>55.451925</td>\n      <td>62.169075</td>\n      <td>2.747925</td>\n      <td>51.030000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>1997</td>\n      <td>82.0</td>\n      <td>69.245775</td>\n      <td>61.659158</td>\n      <td>76.832393</td>\n      <td>6.207233</td>\n      <td>64.917000</td>\n    </tr>\n    <tr>\n      <th>5</th>\n      <td>1998</td>\n      <td>70.0</td>\n      <td>69.585176</td>\n      <td>65.225866</td>\n      <td>73.944487</td>\n      <td>3.566708</td>\n      <td>83.039625</td>\n    </tr>\n    <tr>\n      <th>6</th>\n      <td>1999</td>\n      <td>89.0</td>\n      <td>78.321847</td>\n      <td>71.119057</td>\n      <td>85.524636</td>\n      <td>5.893191</td>\n      <td>77.511195</td>\n    </tr>\n    <tr>\n      <th>7</th>\n      <td>2000</td>\n      <td>88.0</td>\n      <td>82.677016</td>\n      <td>76.320139</td>\n      <td>89.033893</td>\n      <td>5.201081</td>\n      <td>91.417828</td>\n    </tr>\n    <tr>\n      <th>8</th>\n      <td>2001</td>\n      <td>84.0</td>\n      <td>83.272359</td>\n      <td>79.448638</td>\n      <td>87.096080</td>\n      <td>3.128499</td>\n      <td>94.234974</td>\n    </tr>\n    <tr>\n      <th>9</th>\n      <td>2002</td>\n      <td>98.0</td>\n      <td>89.899797</td>\n      <td>84.151660</td>\n      <td>95.647935</td>\n      <td>4.703022</td>\n      <td>90.224579</td>\n    </tr>\n    <tr>\n      <th>10</th>\n      <td>2003</td>\n      <td>91.0</td>\n      <td>90.394889</td>\n      <td>86.961113</td>\n      <td>93.828664</td>\n      <td>2.809453</td>\n      <td>100.350957</td>\n    </tr>\n    <tr>\n      <th>11</th>\n      <td>2004</td>\n      <td>106.0</td>\n      <td>97.417189</td>\n      <td>91.666347</td>\n      <td>103.168031</td>\n      <td>4.705234</td>\n      <td>96.638118</td>\n    </tr>\n    <tr>\n      <th>12</th>\n      <td>2005</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>107.873265</td>\n    </tr>\n    <tr>\n      <th>13</th>\n      <td>2006</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>NaN</td>\n      <td>112.578499</td>\n    </tr>\n  </tbody>\n</table>\n</div>"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 计算预测值y\n",
    "source_df.loc[:12,'yt'] = source_df.apply(lambda x:x['at'] + x['bt'] , axis=1).shift()\n",
    "source_df.loc[13,'yt'] = source_df.loc[12,'yt'] + source_df.loc[11,'bt']\n",
    "\n",
    "source_df"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "由结果可得，2005年和2006年销量分别为107.873265和112.578499"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "data": {
      "text/html": "        <script type=\"text/javascript\">\n        window.PlotlyConfig = {MathJaxConfig: 'local'};\n        if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n        if (typeof require !== 'undefined') {\n        require.undef(\"plotly\");\n        requirejs.config({\n            paths: {\n                'plotly': ['https://cdn.plot.ly/plotly-2.4.2.min']\n            }\n        });\n        require(['plotly'], function(Plotly) {\n            window._Plotly = Plotly;\n        });\n        }\n        </script>\n        "
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# 如果使用online模式，那么生成的图形是有限制的。所以，我们这里先设置为offline模式，这样就避免了出现次数限制问题。\n",
    "cf.set_config_file(offline=True)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "outputs": [
    {
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      "application/vnd.plotly.v1+json": {
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